Comparative advantages of high-order schemes for subsonic, transonic, and supersonic flows

This computational study aims to verify the order of accuracy of the COMPACT and weighted essentially non-oscillatory (WENO) finite difference schemes implemented in the AEROFLO software, and to identify the comparative advantages of these schemes relative to the low-order (MUSCL-based) schemes for a range of flow problems. The method of manufactured solutions was used to determine the order of accuracy of the spatial differencing schemes. The theoretical sixth-order of accuracy is verified for the COMPACT scheme for subsonic flows, while the theoretical fith-order WENO scheme exhibited a 3.5 order of accuracy for supersonic flows. The MUSCL scheme shows the theoretical secondorder accuracy for all flow regimes. The accuracy results were observed for both Cartesian and curvilinear grids. Several subsonic, transonic, and supersonic calculations were then used to evaluate the results from the high- and low-order schemes. For the subsonic and transonic flow configurations, the high-order schemes generally require smaller CPU times, due to their ability to use larger time step sizes or their ability to generate better results with coarser grids as compared to the low-order schemes. For the supersonic flow configurations, both the high- and the low-order schemes capture the shock locations very accurately, although the low-order schemes tend to exhibit significantly larger numerical noise in the regions behind the shocks.